Visitors who wear face veils to Australia's Parliament House have been restricted to sound-proof enclosed galleries usually reserved for noisy school groups under a new counterterrorism security measure.

Some senators accused the Parliament of sending a message to the nation that Muslim women can be treated as second-class citizens.

The government department that runs Parliament House said in a statement on Thursday that "persons with facial coverings" would no longer be allowed in the open public galleries of the House of Representatives or the Senate.

They will be directed to the higher galleries where they could sit behind sound-proof glass.